On multidimensional inverse scattering for stark hamiltonians

Based on the Enss-Weder ["The geometrical approach to multidimensional inverse scattering," J. Math. Phys. 36, 3902-3921 (1995)] time-dependent method, we study one of multidimensional inverse scattering problems for Stark Hamiltonians. We first show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the potential such as vertical bar x vertical bar(-gamma) with gamma > 1/2 which is short range under the Stark effect. This is an improvement of previous results obtained by Nicoleau ["Inverse scattering for Stark Hamiltonians with short-range potentials," Asymptotic Anal. 35, 349-359 (2003)] and Weder ["Multidimensional inverse scattering in an electric field," J. Funct. Anal. 139, 441-465 (1996)]. Moreover, we prove that for a given long-range part of the potential under the Stark effect, the high velocity limit of the Dollard-type modified scattering operator determines uniquely the short-range part of the potential.(c) 2007 American Institute of Physics.